Ladder-type band-pass filter end sections



Aus. 5, 1969 w. THELEN 3,460,073

LADDER-TYPE BAND-PASS FILTER END SECTIONS ald A 7' TOR/VE? Aug. 5, 1969 w. THELEN 3,450,073

LADDER-TYPE BAND-PASS FILTER END SECTIONS Filed April 20, 1967 2 Sheets-Sheet a FIG. 5

United States Patent O 3,460,073 LADDER-TYPE BAND-PASS FILTER END SECTIONS William Thelen, Salem, N.H., assignor to Bell Telephone Laboratories, Incorporated, Murray Hill, NJ., a corporation of New York Filed Apr. 20, 1967, Ser. No. 632,227 Int. Cl. Hflh 7/08 U.S. Cl. 333-72 7 Claims ABSTRACT F THE DISCLOSURE An end section for high frequency band-pass filters minimizes ripple in the pass band response and has either a II-type or a T-type configuration in which the outer arm on the terminating side is a capacitance shunted by the series combination of an inductance and a capacitance, -the interposed inner arm is a capacitance shunted by the series combination of an inductance and a capacitance, and the outer arm on the other side is a capacitance. The impedance relationships of the three arms are defined by the pole-zero pattern of the open and short circuit irnpedance at both sides of the end section.

BACKGROUND OF THE `INVENTION This invention relates generally to band-pass filters and more particularly to high frequency band-pass filter end or terminating sections.

Separately designed end sections aie normally used in multisection -filters because image impedance tend to vary widely with frequency within the pass bands of most filter sections. In the past, half or L-type filter sections having the same pass bands as the full filter sections with which they are used have been employed as end sections to provide reasonable matches to resistive loads. Such end sections have not been completely successful, however, in minimizing pass band ripple at their terminating sides because of their inability to control their terminating side image impedances closely at both upper and lower edges of the pass band while still affording an opportunity for absorbing parasitic capacities into existing circuit components.

The principal object of the invention is to minimize the pass band ripple and simultaneously permit parastic capacity correction in a high frequency band-pass filter end section by controlling the terminating side image impedance closely at both upper and lower edges of the pass band.

Another and more particular object is to do so in as simple a manner as possible and with favorable component impedance values.

SUMMARY OF THE INVENTION In accordance with the invention, an end or terminating band-pass filter section is given a ladde-r configuration with first and second outer arms and an inner arm interposed between the two outer arms and the impedance relationships of the three arms are defined by the short circuit impedance at opposite sides of the filter section having a common resonant frequency within the pass band and different antiresonant frequencies at respectively opposite edges of the pass band, the open circuit impedances at opposite sides of the filter section having a common antiresonant frequency within the pass band at the common resonant frequency at the short circuit frequencies and different resonant frequencies at respectively opposite edges of the pass band, and the open and short circuit impedances at the terminating s ide of the filter section having a common resonant frequency below "ice the pass band and a common antiresonant frequency above the pass band.

In accordance with a particular feature of the invention, the first outer arm of the filter section takes the for of a capacitance shunted by the series combination of an inductance and a capacitance, the second outer arm takes the form of a capacitance and the interposed inner arm takes the form of a capacitance shunted by the series combination of an inductance and a capacitance. The resulting end section has a minimum amount of ripple within the pass band, the terminating side image impedance is closely controlled at both upper and loweredges of the pass band, and favorable component impedance values may be employed throughout. The several circuit configurations possible are, moreover, readily realizable for small bandwidth to center frequency ratios with only capacitors and piezoelectric crystals, thus permitting the end section to be fabricated readily in integrated circuit form. For larger bandwidth to center frequency ratios, conventional lumped constant circuit components may be used.

In one important embodiment of the invention, the

BRIEF DESCRIPTION `OF THE DRAWING FIG. 1A is a schematic diagram of an embodiment of the invention in the form of a lI-type band-pass filter end section using lumped constant inductors and capacitors.

FIG. 1B is a diagram showing the significant resonant and antiresonant frequencies of the open end short circuit impedances of the embodiment of the invention shown in FIG. 1A.

FIG. 2A is a schematic diagram of an embodiment of the invention in the form of a T-type band-pass filter end section using lumped constant inductors and capacitors.

FIGJZB is a diagram showing the significant resonant and antiresonant frequencies of the open and short circuit impedances of the embodiment of the invention shown in FIG. 2A.

FIGS. 3A, 3B, and 3C a-re curves showing the manner in which the image impedances and image transfer losses of the embodiments of the invention shown in FIGS. 1A and 2A vary with frequency.

FIGS. 4 and 5 are schematic diagrams of narrow band embodiments of the invention in which the respective embodiments of FIGS. 1A and 2A are realized entirely with capacitors and piezoelectric crystals.

FIGS. 6A, 6B, and 6C are schematic diagrams showing how the embodiment of the invention illustrated in FIG. 1A may be modified to absorb al1 parasitic capacitances into existing circuit capacitors.

DETAILED DESCRIPTION The embodiment of the invention illustrated in FIG. 1A is a lI-type band-pass filter end section made up of a pair of shunt arms and an interposed series arm. The shunt arm at the left or terminating side of the end section contains a capacitor 11 shunted by the series combination of an inductor 12 and a capacitor 13. The interposed series arm includes a capacitor 14 shunted by the series combination of an inductor 15 and a capacitor 16. The shunt arm at the right, facing the main body of the band-pass filter with which the end section is used, is merely a capacitor 17. As shown, the impedance of the end section at the terminating side is represented by Z, while that at the other side is represented by Z.

The relationships between the various impedance elements of the three arms in the embodiment of the invention shown in FIG. 1A are defined by the pole-zero plot shown in FIG. 1B, Where Zs and Zo represent the shortcircuit and open-circuit impedances, respectively, at the left or terminating side of the end section and ZS and Zo are the short-circuit and open-circuit impedances, respectively, at the other side. On all four lines of the figure, the abscissa is frequency, a pole or antiresonance is represented by the symbol x, and a zero or resonance is represented by the symbol o. As illustrated, all four quantities have poles at zero frequency and zeros at infinite frequency. `Zs has zero at fm1, a frequency below the pass band of the end section, and a pole at f1, the lower edge of the pass band. Zs also has a zero at fo, a frequency within the pass band, and a pole at fm2, a frequency above the pass band. ZD has a zero at fm1, a pole at fo, a zero at f2, the upper edge of the pass band, and a pole of fm2. Z has zero at f1 and a pole at fo and ZS has a zero at f1 and a pole at fo.

The embodiment of the invention illustrated in FIG. 2A is the T-type equivalent of the H-type band-pass filter end section shown in FIG. 1A and, as shown, includes a pair of series arms and an interposed shunt arm. The series arm at the left or terminating sides of the end section contains a capacitor 21 shunted by the series combination of an inductor 22 and a capacitor 23. The interposed shunt arm includes a capacitor 24 shunted by the series combination of an inductor 25 and a capacitor 26. The series arm at the right, facing the main body of the band-pass filter with which the end section is used, is a capacitor 27. As in FIG. 1A, the impedance of the end section at the terminating end is represented by Z, while that at the other end is represented by Z.

The relationships between the various impedance elements of the three arms in the T-type filter section shown in FIG. 2A are defined by the pole-zero plot shown in FIG. 2B, where the symbol meaning is the same as in FIG. 1B. As illustrated in FIG. 2B, all four quantities have poles at zero frequency and zeroes at infinite frequency. Zo has zero at fm1, a pole at fo, a zero at f2, and a pole at fm2. Zs has a zero at fm1, a pole at f1, a zero at fo, and a pole at Fmg. Zo has zero at f1 and a pole at fo and ZS has a zero at fo and a pole at f2.

The embodiments of the invention illustrated in FIGS. lA and 2A have the same image impedances at both sides and have the same image transfer loss. Comparison of their pole-zero plots shows that, in both, the shortcricuit impedances at opposite sides of the end section have a common zero or resonant frequency at j@ and different poles or antiresonant frequencies at f1 and f2, the opposite edges of the pass band. Similarly, in both, the open circuit impedances at opposite sides of the end section have a common pole or antiresonant frequency at fo and different zeroes or resonant frequencies at f1 and f2. Finally, in both, the open and short circuit impedances at the left-hand or terminating side of the end section have a common zero or resonant frequency at fm1 and a common pole or antiresonant frequency at fm2.

The image impedance at the left or terminating sides of the embodiments of the invention shown in FIGS. 1A and 2A is shown in FIG. 3A. As shown, this image impedance, represented by ZI, is a negative reactance between zero frequency and 12.1 and descends in magnitude from infinity to zero. There is a positive reactance between fl and f1 and increases in magnitude from zero to infinity. ZI is resistive between hand f2 and descends rapidly in magnitude above f1 from infinity to a value which holds with relatively little deviation through fo to a frequency approaching f2. From that point, ZI drops rapidly to zero. ZI is a positive reactance and goes from zero to infinity in magnitude from f2 and fm2. ZI is a negative reactance above fm2 and decreases in magnitude from infinity and approaches zero at infinitely high frequencies.

The effect of the present invention in minimizing pass band ripple at the terminating side of the end sections shown in FIG. 1A and FIG. 2A is clearly illustrated in FIG. 3A. The degree to which the magnitude of ZI is flat with frequency from a frequency just above f1 to a frequency just below f2 depends primarily upon the location of fel and fm2 with respect to f1 and f2. In this manner, the invention affords close control of the image impedance at the terminating side of the end sections at both edges of the pass band rather than at only one as afforded by much of the prior art. At the same time, the invention permits ready attainment of this result with a relatively simple circuit configuration and with relatively favorable component impedance values.

The image impedance at the other sides of the embodiments of the invention shown in FIGS. lA and 2A is illustrated in FIG. 3B. As shown, this image impedance, represented by ZI', is a negative reactance between zero frequency and f1 and descends in magnitude from infinity to zero. It is resistive between f1 and f2 and increases from zero to infinity. Above f2, Z1 is a negative reactance dropping from infinity at f2 until it approaches zero at infinitely high frequencies. This characteristic produces an exact match to the image impedances of most full band-pass filter sections with which the end sections are likely to be used.

The manner in which the image transfer loss of the embodiments of the invention shown in FIGS. 1A and 2A Varies with frequency is illustrated in FIG. 3C. As shown, there are loss peaks at fel and faz. There is minimum loss in the pass band from f1 to f2.

Although band-pass filter end sections embodying the invention are shown in FIGS. 1A and 2A as they may be realized for broad band applications with lumped constant inductors and capacitors, they may be realized with capacitors and piezoelectric crystals as well for high frequency applications requiring relatively narrow pass bands. Such end sections are particularly well suited for fabrication in integrated circuit form.

FIG. 4 illustrates an embodiment of the invention which -is an all crystal and capacitor equivalent of the II-type end section shown in FIG. 1A. Since the lumped constant equivalent circuit of a piezoelectric crystal is simply a capacitor shunted by the 'series combination of an inductor and another capacitor, the left or terminating side shunt arm in FIG. 4 is a piezoelectric crystal 41 and the interposed series arm is a piezoelectric crystal 42. The shunt arm on the other side is, as before, simply a capacitor 17. The relationships between the impedances in the various arms of the embodiment of the invention shown in FIG. 4 are defined by the pole-zero plot illustrated in FIG. 1B.

FIG. 5 illustrates an embodiment of the invention which is an all crystal and capacitor equivalent of the T-type end section shown in FIG. 2A. The left or terminating side series arm in FIG. 5 is a piezoelectric crystal 51 and the interposed shunt arm is a piezoelectric crystal 52. The series arm on the other side is, as in FIG. 2A, simply a capacitor 27. The relationships between the impedances of the various arms of the embodiment of the invention shown in FIG. 5 are given by lthe pole-zero plot of FIG. 2B.

A significant additional advantage of the embodiment of the invention illustrated in FIG. lA is that the schematic diagram is susceptible of modification to absorb parasitic capacities into the capacities of actual circuit capacitors. The manner in which this may be done is shown in FIGS. 6A, 6B, and 6C. These figures represent three successive steps of modification and involve only simple Norton transforms.

In FIG. 6A, capacitors 11 in FIG. 1A has been replaced by two parallel capacitors 61 and 62. Nothing else has been changed. FIG. 6B shows the next step in the modifications, where each capacitor shunted by the series combination of an inductor and a capacitor has been replaced by a capacitor in series with the parallel combination of an inductor and a capacitor. Thus, the combination of capacitor 61 shunted by the series combination of inductor 12 and capacitor 13 has been replaced by the combination of capacitor 63 in series with the parallel combination of inductor 64 and capacitor 65. Similarly, the combination of capacitor 14 shunted by the series combination of inductor 15 and capacitor 16 has been replaced -by the combination of capacitor 66 in series with the parallel combination of inductor 67 and capacitor 68. The final step in the transformation is shown in FIG. 6C, Where the combination made up of shunt capacitor 17 to the right of series capacitor 66 has been replaced by the combination made up of a shunt capacitor 69 to the left of a series capacitor 70. The impedance level at the right-hand side of the filter section is changed only by a scaling factor @2.

As can -be seen from an inspection of FIG. 6C, each important parasitic capacity of the end section as transformed appears in parallel with an actual circuit capacitor. The capacitive values of the circuit capacitors may, therefore, be fixed so that the nal desired capacity values are provided by their own capacities in combination with the parasitic capacities. A higher order of accuracy in filter design than heretofore is thereby made possible.h

I claim:

1. A band-pass ladder-type filter section having first and second outer arms, an inner arm interposed between said first and second outer arms, a single pass band, and single loss peaks both above and below said pass band in frequency wherein said first outer arm comprises a capacitance shunted by the series combination of an inductance and a capacitance, said second outer arm comprises a capacitance, said interposed inner arm comprises a capacitance shunted by the series combination of an inductance and a capacitance, the short circuit impedances at opposite ends of said filter section have a cornmon resonant frequency within said pass band and different antiresonant frequencies defining respectively opposite edges of said pass band, the open circuit impedances at opposite ends of said filter section have a common antiresonant frequency within said pass band at the common resonant frequency of the short circuit impedances and different resonant frequencies defining respectively -opposite edges of said pass band, and the open and short circuit impedances at the end of said filter section formed by said first outer arms have a common frequency below said pass band and a common antiresonant frequency above said pass band.

2. A band-pass filter section in accordance with claim 1 which is a l'I-type filter section and in which said outer arms are shunt arms and said inner arm is an interposed series arm.

3. A band-pass II-type filter section in accordance with claim 2 in which the elements of said rst shunt arm and said interposed series arm are lumped constant inductors and capacitors.

4. A band-pass II-type lter section in accordance with claim 2 in which said shunt arm and said interposed series arm both comprise piezoelectric crystals.

5. A band-pass filter section in accordance with claim 1 which is a T-type filter section and in `which said outer arms are series arms and said inner arm is an interposed shunt arm.

6. A band-pass T-type filter section in accordance with claim 5 in which the elements of said first series arrn and said interposed shunt arm are lumped constant inductors and capacitors.

7. A band-pass T-type filter section in accordance with claim 5 in which said first series arm and said interposed shunt arm both comprise piezoelectric crystals.

References Cited UNITED STATES PATENTS 1,568,143 1/1926 Elsasser S33-70 2,001,090 5/1935 Bode 333-70 2,662,216 12/ 1953 Klinkhamer 333-70 2,976,604 3/1961 KosOwsky 33372 X HERMAN KARL SAALBACH, Primary Examiner T. J. VEZEAU, Assistant Examiner U.S. Cl. X.R. 333-76 

